--- title: "Using a delay-adjusted case fatality ratio to estimate under-reporting" description: "Using a corrected case fatality ratio, we calculate estimates of the level of under-reporting for any country with greater than ten deaths" status: real-time-report rmarkdown_html_fragment: true update: 2020-08-11 authors: - id: tim_russell corresponding: true - id: joel_hellewell equal: 1 - id: sam_abbott equal: 1 - id: nick_golding - id: hamish_gibbs - id: chris_jarvis - id: kevin_vanzandvoort - id: ncov-group - id: stefan_flasche - id: roz_eggo - id: john_edmunds - id: adam_kucharski ---

Aim

To estimate the percentage of symptomatic COVID-19 cases reported in different countries using case fatality ratio estimates based on data from the ECDC, correcting for delays between confirmation-and-death.

Data availability

The under-reporting estimates for all countries can be downloaded as a single .csv file here.

Similarly, the prevalence estimates can be downloaded as a single .csv file here.

How to cite this work

If you wish to cite this work, please do cite the associated preprint [1]).

Methods Summary

The associated preprint[1], specifically the corresponding supplementary material contains a full description of the methods and limitations used to arrive at the estimates presented here.

Current estimates of under-reporting, prevalence and adjusted case curves along with reported cases

Temporal variation

Figure 1: Temporal variation in reporting rate. We calculate the percentage of symptomatic cases reported on each day a country has had more than ten deaths. We then fit a Gaussian Process (GP) to these data (see Temporal variation model fitting section for details), highlighting the temporal trend of each countries reporting rate. The red shaded region is the 95% CrI of fitted GP.

Prevalence estimates

Country Prevalence median (95% CrI) Total reported cases New reported cases (tallied over last 10 days) Population
Afghanistan 0.11% (0.05% - 0.26%) 22,890 9,231 38,928,341
Albania 0.023% (0.013% - 0.075%) 1,385 286 2,877,800
Algeria 0.027% (0.013% - 0.066%) 10,589 1,455 43,851,043
Andorra 0.69% (0.21% - 2.3%) 852 88 77,265
Argentina 0.12% (0.059% - 0.26%) 27,360 11,954 45,195,777
Armenia 0.77% (0.39% - 1.7%) 14,669 5,993 2,963,234
Australia 0.00097% (0.00057% - 0.0022%) 7,285 112 25,499,881
Austria 0.016% (0.0058% - 0.046%) 16,964 370 9,006,400
Azerbaijan 0.099% (0.051% - 0.23%) 8,882 3,893 10,139,175
Bahamas 0.00085% (0.00033% - 0.0049%) 103 1 393,248
Bahrain 0.82% (0.52% - 1.5%) 17,269 6,820 1,701,583
Bangladesh 0.055% (0.028% - 0.12%) 78,052 35,208 164,689,383
Belarus 0.24% (0.15% - 0.45%) 51,816 11,052 9,449,321
Belgium 0.086% (0.044% - 0.2%) 59,711 1,650 11,589,616
Bolivia 0.36% (0.19% - 0.77%) 16,165 7,434 11,673,029
Bosnia and Herzegovina 0.04% (0.015% - 0.16%) 2,831 346 3,280,815
Brazil 1.1% (0.61% - 2.3%) 802,828 337,662 212,559,409
Bulgaria 0.085% (0.04% - 0.22%) 3,086 587 6,948,445
Burkina Faso 0.00077% (0.00029% - 0.0029%) 892 45 20,903,278
Cameroon 0.026% (0.016% - 0.053%) 8,681 3,245 26,545,864
Canada 0.2% (0.11% - 0.42%) 97,519 8,112 37,742,157
Chad 0.0019% (0.00075% - 0.0083%) 848 89 16,425,859
Chile 0.71% (0.43% - 3.8%) 154,092 63,454 19,116,209
China 2.9e-05% (1e-05% - 0.00015%) 84,216 93 1,439,323,774
Colombia 0.19% (0.1% - 0.41%) 43,682 16,994 50,882,884
Congo 0.013% (0.0048% - 0.041%) 745 158 5,518,092
Costa Rica 0.024% (0.013% - 0.064%) 1,538 516 5,094,114
Côte d’Ivoire 0.014% (0.0081% - 0.029%) 4,404 1,654 26,378,275
Croatia 0.00089% (3e-04% - 0.0035%) 2,249 4 4,105,268
Cuba 0.0048% (0.0025% - 0.014%) 2,219 214 11,326,616
Cyprus 0.0068% (0.0037% - 0.021%) 975 34 1,207,361
Czechia 0.021% (0.0088% - 0.055%) 9,886 690 10,708,982
Democratic Republic of the Congo 0.005% (0.0024% - 0.015%) 4,514 1,681 89,561,404
Denmark 0.026% (0.012% - 0.069%) 12,035 442 5,792,203
Djibouti 0.33% (0.2% - 0.73%) 4,398 1,484 988,002
Dominican Republic 0.1% (0.059% - 0.22%) 21,437 4,906 10,847,904
Ecuador 0.25% (0.13% - 0.54%) 44,440 5,869 17,643,060
Egypt 0.091% (0.048% - 0.19%) 39,726 17,644 102,334,403
El Salvador 0.067% (0.031% - 0.16%) 3,481 1,203 6,486,201
Equatorial Guinea 0.042% (0.024% - 0.095%) 1,306 263 1,402,985
Estonia 0.041% (0.015% - 0.11%) 1,965 106 1,326,539
Ethiopia 0.0072% (0.0031% - 0.018%) 2,670 1,702 114,963,583
Finland 0.014% (0.0068% - 0.04%) 7,064 288 5,540,718
France 0.052% (0.028% - 0.11%) 155,561 5,893 65,273,512
Gabon 0.08% (0.05% - 0.16%) 3,463 850 2,225,728
Georgia 0.0054% (0.0028% - 0.016%) 831 85 3,989,175
Germany 0.03% (0.015% - 0.064%) 185,674 4,478 83,783,945
Ghana 0.018% (0.011% - 0.033%) 10,358 2,742 31,072,945
Greece 0.015% (0.0063% - 0.043%) 3,088 179 10,423,056
Guatemala 0.28% (0.13% - 0.66%) 8,561 3,954 17,915,567
Guinea 0.011% (0.0071% - 0.022%) 4,372 716 13,132,792
Guyana 0.0038% (0.0013% - 0.021%) 158 8 786,559
Haiti 0.049% (0.027% - 0.12%) 3,941 2,357 11,402,533
Honduras 0.19% (0.085% - 0.47%) 7,669 2,783 9,904,608
Hungary 0.029% (0.013% - 0.072%) 4,039 198 9,660,350
Iceland 0.0014% (0.00076% - 0.004%) 1,807 2 341,250
India 0.057% (0.031% - 0.12%) 297,535 123,772 1,380,004,385
Indonesia 0.033% (0.017% - 0.068%) 35,295 10,079 273,523,621
Iran 0.18% (0.094% - 0.36%) 180,176 33,508 83,992,953
Iraq 0.21% (0.11% - 0.45%) 16,675 10,802 40,222,503
Ireland 0.08% (0.034% - 0.22%) 25,238 362 4,937,796
Isle of Man 0% (0% - 0%) 336 0 85,032
Israel 0.049% (0.026% - 0.11%) 18,701 1,714 8,655,541
Italy 0.11% (0.057% - 0.22%) 236,142 3,894 60,461,828
Japan 0.0026% (0.0012% - 0.0065%) 17,332 528 126,476,458
Kazakhstan 0.038% (0.024% - 0.074%) 13,872 3,490 18,776,707
Kenya 0.011% (0.0048% - 0.029%) 3,215 1,470 53,771,300
Kosovo 0.042% (0.02% - 0.12%) 1,326 278 1,810,366
Kuwait 0.45% (0.28% - 0.82%) 34,432 9,248 4,270,563
Kyrgyzstan 0.016% (0.0088% - 0.041%) 2,166 444 6,524,191
Latvia 0.0068% (0.0025% - 0.023%) 1,094 30 1,886,202
Lebanon 0.0087% (0.0044% - 0.027%) 1,402 230 6,825,442
Liberia 0.021% (0.0059% - 0.081%) 410 137 5,057,677
Lithuania 0.023% (0.0096% - 0.076%) 1,752 90 2,722,291
Luxembourg 0.023% (0.01% - 0.061%) 4,052 40 625,976
Malaysia 0.0041% (0.0026% - 0.0082%) 8,369 637 32,365,998
Mali 0.023% (0.01% - 0.054%) 1,722 496 20,250,834
Mauritania 0.18% (0.072% - 0.48%) 1,162 739 4,649,660
Mauritius 5e-04% (2e-04% - 0.003%) 337 2 1,271,767
Mexico 0.94% (0.51% - 1.9%) 133,974 49,347 128,932,753
Moldova 0.44% (0.22% - 0.94%) 10,727 2,831 4,033,963
Morocco 0.0046% (0.0029% - 0.0099%) 8,537 823 36,910,558
Netherlands 0.075% (0.036% - 0.17%) 48,251 2,125 17,134,873
New Zealand 0% (0% - 0%) 1,154 0 4,822,233
Nicaragua 0.031% (0.014% - 0.18%) 1,464 705 6,624,554
Niger 0.00049% (0.00013% - 0.002%) 974 19 24,206,636
Nigeria 0.01% (0.0051% - 0.023%) 14,554 5,252 206,139,587
North Macedonia 0.63% (0.3% - 1.4%) 3,542 1,412 2,083,380
Norway 0.0092% (0.0044% - 0.039%) 8,594 183 5,421,242
Oman 0.41% (0.26% - 0.74%) 19,954 10,134 5,106,622
Pakistan 0.12% (0.063% - 0.24%) 125,933 59,476 220,892,331
Panama 0.76% (0.38% - 1.7%) 18,586 6,055 4,314,768
Paraguay 0.0094% (0.0057% - 0.02%) 1,230 313 7,132,530
Peru 0.93% (0.5% - 1.9%) 214,788 66,503 32,971,846
Philippines 0.018% (0.0099% - 0.038%) 24,175 7,541 109,581,085
Poland 0.067% (0.032% - 0.16%) 28,201 5,046 37,846,605
Portugal 0.19% (0.093% - 0.43%) 35,910 3,964 10,196,707
Puerto Rico 0.13% (0.077% - 0.28%) 5,352 1,705 2,860,840
Qatar 1.9% (1% - 10%) 75,071 22,164 2,881,060
Romania 0.085% (0.043% - 0.2%) 21,182 2,200 19,237,682
Russia 0.25% (0.15% - 0.49%) 502,436 114,813 145,934,460
San Marino 0.14% (0.077% - 0.59%) 691 20 33,938
Sao Tome and Principe 0.2% (0.1% - 0.62%) 639 176 219,161
Saudi Arabia 0.49% (0.25% - 1%) 116,021 34,255 34,813,867
Senegal 0.018% (0.01% - 0.041%) 4,759 1,330 16,743,930
Serbia 0.018% (0.011% - 0.042%) 12,102 748 8,737,370
Sierra Leone 0.01% (0.0044% - 0.032%) 1,085 256 7,976,985
Singapore 0.21% (0.12% - 0.62%) 39,387 5,527 5,850,343
Sint Maarten 0% (0% - 0%) 77 0 42,882
Slovakia 0.001% (5e-04% - 0.003%) 1,541 21 5,459,643
Slovenia 0.0076% (0.0025% - 0.023%) 1,488 15 2,078,932
Somalia 0.013% (0.006% - 0.037%) 2,513 685 15,893,219
South Africa 0.27% (0.15% - 0.56%) 58,568 29,328 59,308,690
South Korea 0.0029% (0.0014% - 0.0083%) 12,003 562 51,269,183
South Sudan 0.014% (0.0071% - 0.037%) 1,604 610 11,193,729
Spain 0.022% (0.012% - 0.097%) 242,707 3,479 46,754,783
Sri Lanka 0.0032% (0.0019% - 0.0069%) 1,877 319 21,413,250
Sudan 0.059% (0.027% - 0.14%) 6,730 2,209 43,849,269
Sweden 0.72% (0.38% - 1.5%) 48,288 11,812 10,099,270
Switzerland 0.016% (0.0074% - 0.039%) 30,961 216 8,654,618
Tajikistan 0.027% (0.017% - 0.049%) 4,834 1,271 9,537,642
Thailand 0.00018% (9.1e-05% - 0.00049%) 3,125 49 69,799,978
Togo 0.0028% (0.0015% - 0.0082%) 524 96 8,278,737
Tunisia 0.00052% (0.00018% - 0.0023%) 1,087 16 11,818,618
Turkey 0.035% (0.019% - 0.072%) 174,023 11,903 84,339,067
Ukraine 0.064% (0.031% - 0.15%) 29,070 5,866 43,733,759
United Arab Emirates 0.16% (0.1% - 0.3%) 40,986 7,816 9,890,400
United Kingdom 0.45% (0.24% - 0.92%) 291,409 20,187 67,886,004
United Republic of Tanzania 0% (0% - 0%) 509 0 59,734,213
United States of America 0.44% (0.24% - 0.89%) 2,023,347 276,260 331,002,647
Uruguay 0.0033% (0.0012% - 0.011%) 847 31 3,473,727
Uzbekistan 0.0081% (0.0051% - 0.016%) 4,819 1,306 33,469,199
Venezuela 0.011% (0.0066% - 0.023%) 2,814 1,445 28,435,943
Yemen 0.049% (0.022% - 0.11%) 591 304 29,825,968

Table 1: Estimates for the prevalence of COVID-19 in each country with greater than 10 deaths. We use the under-reporting estimates to adjust the reported case curves and tally these up over the last ten days as a proxy for prevalence. See Detailed Methods for more details.

Adjusted symptomatic case estimates

Figure 2: Estimated number of new symptomatic cases, calculated using our temporal under-reporting estimates. We adjust the reported case numbers each day - for each country with an under-reporting estimate - using our temporal under-reporting estimates to arrive at an estimate of the true number of symptomatic cases each day. The shaded blue region represents the 95% CrI, calcuated directly using the 95% CrI of the temporal under-reporting estimate.

Reported cases

Figure 3: Reported number of cases each day, pulled from the ECDC and plotted against time for comparison with our estimated true numbers of symptomatic cases each day, adjusted using our under-reporting estimates.

Current under-reporting estimates

Country Percentage of symptomatic cases reported (95% CI) Total cases Total deaths
Afghanistan 58% (41%-76%) 37,054 1,312
Albania 32% (22%-45%) 6,536 200
Algeria 72% (56%-88%) 35,712 1,312
Andorra 60% (23%-100%) 963 52
Angola 22% (15%-30%) 1,672 75
Argentina 52% (45%-58%) 246,486 4,634
Armenia 75% (61%-90%) 40,433 796
Australia 43% (32%-57%) 21,397 313
Austria 96% (77%-100%) 22,122 723
Azerbaijan 89% (77%-100%) 33,647 492
Bahamas 85% (54%-100%) 945 15
Bahrain 99% (93%-100%) 44,397 163
Bangladesh 98% (87%-100%) 260,507 3,438
Belarus 45% (29%-66%) 68,947 589
Belgium 98% (91%-100%) 74,527 9,879
Benin 74% (49%-99%) 1,936 38
Bolivia 28% (24%-32%) 91,635 3,712
Bosnia and Herzegovina 43% (32%-57%) 14,498 425
Brazil 62% (56%-69%) 3,057,470 101,752
Bulgaria 38% (27%-50%) 13,512 459
Burkina Faso 82% (39%-100%) 1,211 54
Cameroon 93% (58%-100%) 18,042 395
Canada 96% (83%-100%) 120,117 8,987
Cape Verde 86% (55%-100%) 2,883 32
Central African Republic 93% (58%-100%) 4,641 60
Chad 70% (14%-100%) 945 76
Chile 83% (38%-100%) 375,044 10,139
China 94% (24%-100%) 88,906 4,690
Colombia 39% (35%-44%) 397,623 13,154
Congo 94% (74%-100%) 3,664 58
Costa Rica 74% (50%-99%) 23,872 244
Cote dIvoire 99% (93%-100%) 16,798 105
Croatia 70% (41%-99%) 5,649 158
Cuba 90% (55%-100%) 3,046 88
Cyprus 87% (57%-100%) 1,252 19
Czechia 98% (87%-100%) 18,494 389
Democratic Republic of the Congo 69% (29%-100%) 9,488 223
Denmark 93% (73%-100%) 14,815 620
Djibouti 93% (73%-100%) 5,347 59
Dominican Republic 96% (80%-100%) 80,499 1,328
Ecuador 51% (42%-60%) 94,701 5,932
Egypt 32% (26%-38%) 95,666 5,035
El Salvador 41% (31%-53%) 20,872 570
Equatorial Guinea 75% (47%-100%) 4,821 83
Estonia 80% (39%-100%) 2,158 63
Eswatini 55% (38%-76%) 3,309 61
Ethiopia 54% (44%-64%) 23,591 420
Finland 84% (36%-100%) 7,601 333
France 94% (81%-99%) 202,775 30,340
Gabon 98% (90%-100%) 8,006 51
Georgia 86% (56%-100%) 1,264 17
Germany 99% (96%-100%) 217,293 9,201
Ghana 99% (94%-100%) 41,212 215
Greece 80% (50%-100%) 5,749 213
Guatemala 37% (31%-45%) 56,987 2,222
Guinea 97% (86%-100%) 7,930 50
Guinea Bissau 70% (39%-99%) 2,052 29
Guyana 48% (24%-87%) 568 22
Haiti 21% (10%-39%) 7,649 183
Honduras 52% (41%-64%) 47,872 1,506
Hungary 48% (22%-88%) 4,731 605
Iceland 88% (55%-100%) 1,962 10
India 100% (100%-100%) 2,268,675 45,257
Indonesia 40% (35%-47%) 127,083 5,765
Iran 19% (17%-22%) 328,844 18,616
Iraq 50% (44%-58%) 153,599 5,464
Ireland 39% (23%-61%) 26,768 1,772
Israel 99% (94%-100%) 85,222 613
Italy 52% (41%-66%) 250,825 35,209
Jamaica 75% (31%-100%) 1,031 14
Japan 100% (98%-100%) 48,238 1,051
Jersey 34% (8.5%-94%) 347 31
Jordan 84% (49%-100%) 1,268 11
Kazakhstan 94% (84%-99%) 100,164 1,269
Kenya 81% (66%-95%) 26,928 423
Kosovo 34% (25%-48%) 10,419 341
Kuwait 99% (93%-100%) 72,400 482
Kyrgyzstan 92% (31%-100%) 40,455 1,478
Latvia 51% (27%-90%) 1,293 32
Lebanon 90% (66%-100%) 6,812 80
Lesotho 37% (20%-65%) 781 24
Liberia 50% (12%-100%) 1,240 79
Libya 43% (33%-57%) 5,541 120
Lithuania 63% (32%-99%) 2,265 81
Luxembourg 96% (82%-100%) 7,216 121
Madagascar 91% (73%-100%) 13,202 151
Malawi 33% (23%-45%) 4,673 146
Malaysia 93% (55%-100%) 9,094 125
Maldives 96% (82%-100%) 5,157 19
Mali 77% (36%-100%) 2,573 125
Mauritania 98% (79%-100%) 6,498 157
Mexico 14% (12%-16%) 485,836 53,003
Moldova 53% (43%-65%) 27,841 850
Montenegro 69% (49%-95%) 3,696 68
Morocco 47% (36%-61%) 34,063 516
Mozambique 90% (65%-100%) 2,411 16
Namibia 86% (59%-100%) 3,101 19
Nepal 96% (66%-100%) 23,310 79
Netherlands 98% (88%-100%) 59,139 6,148
New Zealand 61% (26%-99%) 1,220 22
Nicaragua 76% (37%-100%) 3,902 123
Niger 67% (23%-100%) 1,158 69
Nigeria 93% (80%-100%) 46,867 950
North Macedonia 40% (31%-51%) 11,965 528
Norway 88% (55%-100%) 9,638 256
Oman 81% (33%-100%) 81,787 521
Pakistan 96% (86%-100%) 285,191 6,112
Palestine 99% (94%-100%) 19,121 110
Panama 59% (49%-72%) 75,394 1,664
Paraguay 86% (53%-100%) 7,234 82
Peru 93% (34%-100%) 483,133 21,276
Philippines 100% (100%-100%) 136,638 2,293
Poland 64% (50%-80%) 52,410 1,809
Portugal 94% (47%-100%) 52,825 1,759
Puerto Rico 89% (57%-100%) 22,818 279
Qatar 82% (37%-100%) 113,262 188
Romania 34% (29%-41%) 62,547 2,729
Russia 58% (51%-65%) 897,599 15,131
San Marino 73% (9.5%-100%) 717 42
Sao Tome and Principe 87% (55%-100%) 878 15
Saudi Arabia 40% (32%-50%) 289,947 3,199
Senegal 51% (36%-69%) 11,312 236
Serbia 74% (51%-95%) 28,262 646
Sierra Leone 83% (39%-100%) 1,917 69
Singapore 94% (72%-100%) 55,292 27
Sint Maarten 31% (10%-87%) 189 17
Slovakia 91% (67%-100%) 2,599 31
Slovenia 69% (35%-99%) 2,255 120
Somalia 92% (58%-100%) 3,227 93
South Africa 44% (39%-50%) 563,598 10,621
South Korea 93% (62%-100%) 14,660 305
South Sudan 76% (50%-99%) 2,470 47
Sri Lanka 96% (81%-100%) 2,871 11
Sudan 26% (17%-39%) 11,956 781
Suriname 89% (65%-100%) 2,489 30
Sweden 87% (72%-99%) 82,972 5,766
Switzerland 97% (86%-100%) 36,619 1,711
Syria 23% (14%-42%) 1,188 52
Tajikistan 97% (71%-100%) 7,827 62
Thailand 84% (52%-100%) 3,351 58
Togo 72% (27%-100%) 1,067 25
Tunisia 88% (53%-100%) 1,717 51
Turkey 87% (71%-100%) 241,997 5,858
Ukraine 47% (38%-58%) 83,115 1,951
United Arab Emirates 97% (78%-100%) 62,704 357
United Kingdom 18% (15%-21%) 311,641 46,526
United States of America 99% (98%-100%) 5,094,394 163,461
Uruguay 50% (30%-82%) 1,364 37
Uzbekistan 99% (92%-100%) 31,545 202
Venezuela 97% (88%-100%) 25,805 223
Yemen 6.7% (3.7%-11%) 1,832 518
Zambia 16% (11%-24%) 8,210 241
Zimbabwe 40% (30%-52%) 4,748 104

Table 2: Estimates for the proportion of symptomatic cases reported in different countries using cCFR estimates based on case and death timeseries data from the ECDC. Total cases and deaths in each country is also shown. Confidence intervals calculated using an exact binomial test with 95% significance.

Adjusting for outcome delay in CFR estimates

During an outbreak, the naive CFR (nCFR), i.e. the ratio of reported deaths date to reported cases to date, will underestimate the true CFR because the outcome (recovery or death) is not known for all cases [6]. We can therefore estimate the true denominator for the CFR (i.e. the number of cases with known outcomes) by accounting for the delay from confirmation-to-death [2].

We assumed the delay from confirmation-to-death followed the same distribution as estimated hospitalisation-to-death, based on data from the COVID-19 outbreak in Wuhan, China, between the 17th December 2019 and the 22th January 2020, accounting right-censoring in the data as a result of as-yet-unknown disease outcomes (Figure 1, panels A and B in [8]). The distribution used is a Lognormal fit, has a mean delay of 13 days and a standard deviation of 12.7 days [8].

To correct the CFR, we use the case and death incidence data to estimate the proportion of cases with known outcomes [2,7]:

\[ u_{t} = \frac{ \sum_{j = 0}^{t} c_{t-j} f_j}{c_t}, \]

where \(u_t\) represents the underestimation of the proportion of cases with known outcomes [2,6,7] and is used to scale the value of the cumulative number of cases in the denominator in the calculation of the cCFR, \(c_{t}\) is the daily case incidence at time, \(t\) and \(f_t\) is the proportion of cases with delay of \(t\) between confirmation and death.

Approximating the proportion of symptomatic cases reported

At this stage, raw estimates of the CFR of COVID-19 correcting for delay to outcome, but not under-reporting, have been calculated. These estimates range between 1% and 1.5% [2–4]. We assume a CFR of 1.4% (95% CrI: 1.2-1.7%), taken from a recent large study [4], as a baseline CFR. We use it to approximate the potential level of under-reporting in each country. Specifically, we perform the calculation \(\frac{1.4\%}{\text{cCFR}}\) of each country to estimate an approximate fraction of cases reported.

Temporal variation model fitting

We estimate the level of under-reporting on every day for each country that has had more than ten deaths. We then fit a Gaussian Process (GP) model using the library greta and greta.gp. The parameters we fit and their priors are the following: \[ \begin{aligned} &\sigma \sim \text{Log Normal(-1, 1)}: \quad &\text{Variance of the reporting kernel} \\ &\text{L} \sim \text{Log Normal(4, 0.5)}: \quad &\text{Lengthscale of the reporting kernel} \\ &\sigma_{\text{obs}} \sim \text{Truncated Normal(0, 0.5)}, \quad &\text{Variance of the obseration kernel, truncated at 0} \end{aligned} \] The kernel is split into two components: the reporting kernel \(R\), and the observation kernel \(O\). The reporting component has a standard squared-exponential form. For the observation component, we use an i.i.d. noise kernel to acccount for observation overdispersion, which can smooth out overly clumped death time-series. This is important as some countries have been known to report an unusually large number of deaths on a single day, due to past under-reporting.

In the sampling and fitting process, we calculate the expected number of deaths at each time-point, given the baseline CFR. We then use a Poisson likelihood, where the expected number of deaths is the rate of the Poisson likelihood, given the observed number of deaths

Approximating prevalence

We use the adjusted case curves, adjusted for under-reporting and for asymptomatic infections as a proxy for prevalence. Specifically, we tally up the adjusted new cases each day over the last ten days and calculate what percentage of the population in question this total equates to. This serves as a crude prevalence estimate. We assume ten days of infectiousness as taken from the mean of the total infectious period [9].

Adjusting case counts for under-reporting

We adjust the reported number of cases each day, pulled from the ECDC. Specifically, we divide the case numbers of each day by our “proportion of cases reported” estimates that we calculate each day for each country.*

Limitations

Implicit in assuming that the under-reporting is \(\frac{1.4\%}{\text{cCFR}}\) for a given country is that the deviation away from the assumed 1.4% CFR is entirely down to under-reporting. In reality, burden on healthcare system is a likely contributing factor to higher than 1.4% CFR estimates, along with many other country specific factors.

The following is a list of the other prominent assumptions made in our analysis:

Code and data availability

The code is publically available at https://github.com/thimotei/CFR_calculation. The data required for this analysis is a time-series for both cases and deaths, along with the corresponding delay distribution. We scrape this data from ECDC, using the NCoVUtils package [10].

The under-reporting estimates for all countries can be downloaded as a single .csv file here.

Similarly, global prevalence estimates can be downloaded as a single .csv file here

Acknowledgements

The authors, on behalf of the Centre for the Mathematical Modelling of Infectious Diseases (CMMID) COVID-19 working group, wish to thank DSTL for providing the High Performance Computing facilities and associated expertise that has enabled these models to be prepared, run and processed and in an appropriately-rapid and highly efficient manner.

References

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